{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "q8vHMOtbxH4y"
      },
      "source": [
        "Copyright 2022 Google LLC\n",
        "\n",
        "Licensed under the Apache License, Version 2.0 (the \"License\");\n",
        "you may not use this file except in compliance with the License.\n",
        "You may obtain a copy of the License at\n",
        "\n",
        "     https://www.apache.org/licenses/LICENSE-2.0\n",
        "\n",
        "Unless required by applicable law or agreed to in writing, software\n",
        "distributed under the License is distributed on an \"AS IS\" BASIS,\n",
        "WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
        "See the License for the specific language governing permissions and\n",
        "limitations under the License."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "gqbG8Fvj1Py2"
      },
      "outputs": [],
      "source": [
        "from jax import numpy as jnp\n",
        "# force double precision\n",
        "from jax import config\n",
        "config.update(\"jax_enable_x64\", True)\n",
        "\n",
        "from matplotlib import pyplot as plt\n",
        "\n",
        "from sobolev import chebyshev\n",
        "from sobolev import utils\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "s2D4cyjr1sEE"
      },
      "outputs": [],
      "source": [
        "x = jnp.linspace(0, 3, 1000)\n",
        "y = jnp.linspace(-5, 5, 1000)\n",
        "\n",
        "X, Y = jnp.meshgrid(x, y)\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "height": 1000
        },
        "executionInfo": {
          "elapsed": 1984,
          "status": "ok",
          "timestamp": 1647354122014,
          "user": {
            "displayName": "",
            "photoUrl": "",
            "userId": ""
          },
          "user_tz": 240
        },
        "id": "7N_WDu6u4cZk",
        "outputId": "2660b94c-0ea1-4bfe-c810-011020683a23"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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akhvpTpJ+RF/fnPYRdF+GuAU4tl/3Lf19U/vvp9O9zq/r1zFWn2jrN/XtBk1Iuq+ZXlRV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\nAABJRU5ErkJggg==\n",
            "text/plain": [
              "\u003cFigure size 1000x800 with 2 Axes\u003e"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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5/Xm/czWb4PPzqvqn+Wxssqr6HN3PXixr4955zve7SFb6m5dWrnG/diStfP1V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\n",
            "text/plain": [
              "\u003cFigure size 1000x800 with 2 Axes\u003e"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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Dsn/cr2dG/bOqvgbcCZw/ZBAYMyvv0wm8kS5wXk8X7j85xbzHAWuS3ER3su6KcYeNAKiq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\nkiSpGQYfSZLUDIOPJElqhsFHkiQ14/8HmiN06GOBJQgAAAAASUVORK5CYII=\n",
            "text/plain": [
              "\u003cFigure size 1000x800 with 2 Axes\u003e"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
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jeL3Rut0mcznZzBrktU+DNJPX4UzNaNVvOi8Qn1f+93PB9lR7dQw+0qZlMj/u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\nRU5ErkJggg==\n",
            "text/plain": [
              "\u003cFigure size 1000x800 with 2 Axes\u003e"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "for degree in [10, 100, 500, 1000]:\n",
        "  plt.figure(figsize=(10, 8))\n",
        "  plt.title('Region of convergence of Chebyshev polynomials of degree %s' % degree)\n",
        "  Z = jnp.abs(special.eval_chebyt(degree, X + Y * 1j, normalization='residual', low=0.01, high=2.))\n",
        "  Z = Z.at[Z \u003e 1].set(jnp.nan)\n",
        "  plt.contourf(X, Y, jnp.log(Z))\n",
        "  plt.xlabel('Real(z)')\n",
        "  plt.ylabel('Im(z)')\n",
        "  plt.colorbar()\n",
        "  plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "pPKna5oH51tY"
      },
      "outputs": [],
      "source": [
        "def rec_extragradient_residual(step: float, momentum: float):\n",
        "  \"\"\"Recurrence for the Residual Chebyshev polynomial.\"\"\"\n",
        "  # Reference: https://fa.bianp.net/blog/2020/polyopt/\n",
        "  while True:\n",
        "    yield 1 + momentum, -step, step * step, - momentum\n",
        "\n",
        "def extragradient_residual(n, x, step, momentum):\n",
        "  coefs = rec_extragradient_residual(step, momentum)\n",
        "  return utils.eval_four_term(n, coefs, x)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ZIoxjn6x7O6P"
      },
      "outputs": [],
      "source": [
        "x = jnp.linspace(0, 3, 1000)\n",
        "y = jnp.linspace(-3, 3, 1000)\n",
        "\n",
        "X, Y = jnp.meshgrid(x, y)\n",
        "\n",
        "step = 1\n",
        "momentum = 0.9\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "height": 1000
        },
        "executionInfo": {
          "elapsed": 1535,
          "status": "ok",
          "timestamp": 1647354220362,
          "user": {
            "displayName": "",
            "photoUrl": "",
            "userId": ""
          },
          "user_tz": 240
        },
        "id": "3MJF2v5Z7Ras",
        "outputId": "c43092fb-e81e-465e-caef-5dd4944f561c"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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NneX+XZo2zR/StMl/kOaA2c+zaX4dXkNzEHhdZp61gPL9kKbH+yvKel9Fc6bSpjEX8Uqa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\nMdxIkqSqGG4kSVJVDDeSJKkq/x9EIi4/MXf6dQAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "\u003cFigure size 1000x800 with 2 Axes\u003e"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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ZmfmTBSpbVYYFgn4hYj6DzSCXb9yL/Vdt2ma9R668eJuyPXW3c7eabub1HLj6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\n4UaSJFXl/wP5aCHFnmFb7QAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "\u003cFigure size 1000x800 with 2 Axes\u003e"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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MJdiM25l4nOnGCThgLY4kaXEb+8aZEbEKOBjYE7gVuAA4KzN/tkBlq8qwQNAv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\nSUVORK5CYII=\n",
            "text/plain": [
              "\u003cFigure size 1000x800 with 2 Axes\u003e"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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tUJPUKB2KB81vwJEkTTrDzRhdctWeIwWb+b6Td/fyDTiSpElmuBmTfmFhWLCZ\nq47E3csZNeAYciRJi53hZoENCgizCTajdiYeZbpRAg5YiyNJWtxGvnFmRKwBDgH2BG4BLgDOysyf\nzFPZqjIoEPQKEXMZbPq5fMPu7LNy41brPWLFxVuV7ak7n7vFdJ3Xs9+qa7apDJIkzbWh4SYingu8\nFPgBcA5wCbAD8JvAcRFxAfCazLxyHss5sbY11MDowab7lgvdnYqXXbmUW1ffttWyewUcYKuQ0x1w\nYMvXZ9CRJC0Go9Tc7Ag8OjNv6TUyIg4C9gUMN8WwZptRQw2M3semHWx2uexWbrjPsjuea4ecfgEH\nGLkWB7auyQGDjiRpcRgabjLz3QARsSozr2qPi4gVmXnePJVtoswm0MDsQs2w5qgb7rPsjse9Tgnv\nFXA66+xXiwNb1+RA75ADBh1J0viM3OcG+EFEfAR4fmbeXJ77FDBVNyaaSWfamQYaGF5T0y/YdEJM\nuwZn0LVuBgUc2LoWB/o3V7UNq9HpMPBIkubLTMLNt4EvAV+KiKdn5mXA4FtPV2AuwgxsW6DpGKUD\n8bC7gXcvr1fA6S7ToNocmHnYAQOPJGn+zCTcZGb+U0R8C/iPiDgOyGEzTYq5CjEw/KJ7M71Wzbae\nFTXKsvuFHNi6vMPCDtwZePptK2t4JEnzZSbhJgAy878j4nHAh4FtunRuRBwJvBPYDvjXzHzLtiyv\nn9lcl2VbA0zHTILMfIaY2a57UNNVt3boGbR9jlhx8cihZ9T3zhAkSXWLiFcAbwN2z8xNg6adSbg5\nqvMgM6+NiMOAR82uiBAR2wHvBo4ANgDfjIhPZuZ3ZrO8mQaY2TYhtW3L1YLHGWRmolc5R2nK6mef\nlRsHbt9e/Xq6jVrrA4YeSapBRKyiyQsjnZk9ynVu/gA4KTOvbT+fmbcDZ0fEfYA9MvPLMyzrw4BL\nM/P7ZT0fAo4GBoabN134+L79ODpmc2+mubitwWwDS69TtheDfuWayevsd9r5MO+dZZ+fjs4+0m9/\nMfRI0kT5e+CVwGmjTDxKzc2vAf8TEefQXMRvI81F/O4LPAbYBPzVLAq6F9A+tXwD8PDuiSLiWOBY\ngNWrVwMr7hjXCTFzcf+luaxJmUlYaZ/dtJhCzmzLtfyK3Oq6Otvqcga/n+/t8X6fufLOfaJ9vZ52\n6Fl7wOnbXDZJ0kh2i4j1reF1mblulBkj4onA1Zn5rYjRvh9Huc7NOyPiXcBhwKOBA2luv3ARcMw2\nXJm4Vwm36qBcXvw6gDVr1uTaA06/owmi80W11S/z+zX/ZnQq9sotB7etJmf0L/TFEGR6mW25OvMN\n6qA8TK/T0Lv1a7bq3hf6XVnZYCNJW4vbYr66TWzKzDV91xtxFu3aizutBV4N/NZMVjZSn5vM/CVw\nZvmbKxuAVa3hlcBIbQXDmhS6w0+39vN9+96UL8/Z9L8Z9Yt9UvrdtM0mtIwSVmDm/Wz6ae8fa0ee\nS5I0Lpl5eK/nI+KBwL2ATq3NSuDciHhYZl7Xb3kzuXHmvYCXAPu058vMJ466jC7fBPYty70aeCbw\ne7Nc1hYGhZ/ujqcz+dLspRN+hn2B96oJ6hcUFkPomUmIWejwAvaZkaRpkJnfBn69MxwRlwNr5vJs\nqU8A7wP+A/jVzIu4pcy8PSJeDHyW5lTwEzLzwm1d7jAzCT4w+Ev3o5sP7vuF3V3j0ysA9Gv66g4W\n8x125jrIGGIkSeM0k3Dz88z8v3O58sz8FM0tHBaFuQg+nWauXl/wgwLPoD4+nfAxHyFnWLAZFmbm\nIsgYYCRJo8jMfUaZbibh5p0R8Trgc8CtrRVtW7vOhOj+Au53XZVeHVo72kFgNkHn1tW3DQw47TOc\nYHin4EHBZlCoGbUzby8GGUnSfJtJuHkgcAzNWVOdZqksw1NnNmFnpkGnXz+dXgGnO9i0n+sVcvoF\nm36hZraBxjAjSVpoMwk3TwbunZmzP8e3YqOEnWFBp1fImUnA6WXUYDOTUDMo0BhmJEnjNpNw8y1g\nV+BH81OUurS/5AcFnWEhp18tTnfA6YSYdg3OtgQbQ40kaVLNJNzcE7g4Ir7Jln1uZnsq+NTofPHP\nJOSMUovTqwZnUD+b2QYbQ40kaZLMJNy8bt5KMSWGhZzZBJxRzXWwMdRIkharkcNNZn5xPgsyTfZb\ndc2sA063mfS/aRsWbAw1kqRJdZdhE0TEjRGxucffjRGxeSEKWaP9Vl3TMyh0h4rumpRRrwY8UwYb\nSVIthoabzFyemTv3+FuemTsvRCFrNpuAM0yv08LbugPSKMs32EiSJsXQcKP5N0rAaRtUe9MJNsMC\nTscofWwMNpKkSWK4WSSGBZxRa29u3Dvu+OsY9d5RBhtJUg0MN4vIbIPEbG98OayfjcFGkjSJDDeL\nTHeg6Fd7M18di/uVQ5KkSWG40Va1NgYbSdIkM9wsQoNqb0bRrzNxvyYpSZJqYriZMKOEktl0Ju6w\n1kaSNOkMN4vUKLU3c9HvZqa1QpIkLXaGmynUr/bHWhtJUg0MN4tYv7AxrGlq1Av4SZJUI8NNJdp9\na9p9bgaxSUqSVCPDzQTZljAyrH+OTVKSpFoYbha5UUPHsiuX3vHYZilJ0jQz3FRi1GYpr28jSaqd\n4WbCzfZ08HYTl01SkqSaGG4mlDUwkiT1ZriZAO2alVE6FdvnRpI0zQw3FRr1VHBJkmpkuJEkSVUx\n3FRoJs1SdiaWJNXGcFMhm6UkSdPMcDOFvO2CJKlmhpsJMZPmo37NUp4+LkmaBoabCtksJUmaZoab\nCTSsWcnr3EiSppnhpkLW3EiSppnhZgr0u/+Up4FLkmpkuJlg/ToI2ywlSZpmhpsK2SwlSZpmhhtJ\nklQVw80EGbWPjM1SkqRpZripkM1SkqRpZripkDU3kqRpZrip0KCaG+8rJUmqneFGkiRVxXBTge6L\n9NksJUmaZoabCtmhWJJUi4g4PiKujojzyt9Rw+ZZshAF08JafkUacCRJNfn7zHz7qBNbczOhBnUM\nNthIkqaZ4aZC9rmRJFXmxRFxfkScEBF3HzaxzVKSJAmA7W6btx/Iu0XE+tbwusxc1xmIiLOAFT3m\nWwv8M/AGIMv/dwDPG7Qyw03Fbl19W99xo97KQZKkObApM9f0G5mZh4+ykIh4L3D6sOlslpowMwkl\ny65cesfjI1ZcPB/FkSRpXkXEHq3BJwMXDJvHmpuKDaq5kSRpQrw1Ig6iaZa6HPiTYTMYbiq27Mql\nBhxJ0kTLzGNmOo/NUhUz2EiSppHhRpIkVcVwI0mSqmK4kSRJVTHcSJKkqhhuJElSVQw3E86L80mS\ntCXDjSRJqorhZoo8dedzx10ESZLm3VjCTUQ8LSIujIhfRUTfG2lJkiTN1Lhqbi4AngKcPab1S5Kk\nSo3l3lKZeRFARIxj9ZIkqWL2uZlC+626ZtxFkCRp3sxbzU1EnAWs6DFqbWaeNoPlHAscC7B69eo5\nKp0kSarVvIWbzDx8jpazDlgHsGbNmpyLZUqSpHrZLDXBPLVbkqStjetU8CdHxAbgkcAZEfHZcZRD\nkiTVZ1xnS50KnDqOdUuSpLrZLCVJkqpiuKncPis3jrsIkiQtKMPNBPI6NZIk9We4kSRJVTHcVOTW\n1beNuwiSJI2d4UaSJFXFcCNJkqpiuJEkSVUx3EyBI1ZcPO4iSJK0YAw3U8bTyCVJtTPcSJKkqhhu\npoR3EJckTQvDTSW8zYIkSQ3DjSRJqorhRpIkVcVwUwFP9ZYk6U6GmwnVOaXbjsKSJG3JcCNJkqpi\nuJEkSVUx3EiSpKoYbiRJUlUMN5IkqSqGmyniTTMlSdPAcCNJkqpiuJEkSVUx3EiSpKoYbiRJUlUM\nN1PAWzRIkiZZRLwkIi6JiAsj4q3Dpl+yEIXS/Nhv1TVcctWeA6fxppqSpEkWEY8FjgYOzMxbI+LX\nh81jzU3F9lm5cdxFkCRpW70QeEtm3gqQmT8aNoPhRpIkLWb3Aw6JiK9HxBcj4qHDZrBZqgJP3flc\nzrxu/3EXQ5KkfnaLiPWt4XWZua4zEBFnASt6zLeWJqvcHXgE8FDglIi4d2Zmv5UZbip16+rbxl0E\nSdKE2e7nyS6X3Tofi96UmWv6jczMw/uNi4gXAh8vYeYbEfErYDegb98Lm6Uq0e44fOPeMcaSSJI0\npz4BHAYQEfcDlgKbBs1gzY0kSVrMTgBOiIgLgNuA5wxqkgLDTVX2WbmRa6/ca9zFkCRpzmTmbcAf\nzGQem6UkSVJVDDcTbr9V18zpdJIkTTrDjSRJqorhpjLdp4B7XylJ0rQx3EiSpKoYbiRJUlUMN5Xo\n1fzkHcElSdPIcCNJkqpiuKnAsNO8PQ1ckjRNDDcVsRlKkiTDTbX2Wdn3ZqmSJFXNcFMxr3EjSZpG\nhhtJklQVw01lbI6SJE07w01FejVDeaaUJGnaGG4q5ZlTkqRpZbipRLuGpvvmmZIkTRPDTWWssZEk\nTTvDTaWeuvO59reRJE0lw01lnrrzuZ4xJUmaaoabilhTI0mS4aZK/3K/k8ZdBEmSxsZwU5mPbj6Y\nj24+2FocSdLUWjLuAmhurT3g9HEXQZKksbLmRpIkVcVwI0mSqmK4kSRJVTHcSJKkqowl3ETE2yLi\n4og4PyJOjYhdx1EOSZJUn3HV3JwJPCAzDwS+C7xqTOWQJEmVGUu4yczPZebtZfBrwMpxlEOSJNVn\nMfS5eR7w6X4jI+LYiFgfEes3bvSeSZIkabB5u4hfRJwFrOgxam1mnlamWQvcDpzYbzmZuQ5YB7Bm\nzZqch6JKkqSKzFu4yczDB42PiOcAjwcel5mGFkmSNCfGcvuFiDgSOA54TGbePI4ySJKkOo2rz827\ngOXAmRFxXkS8Z0zlkCRJlRlLzU1m3ncc65UkSfVbDGdLSZIkzRnDjSRJqorhRpIkVcVwI0mSqmK4\nkSRJVTHcSJKkqhhuJElSVQw3kiSpKoYbSZJUlbFcoViSJGkUEfFhYL8yuCtwfWYeNGgew40kSVq0\nMvMZnccR8Q7ghmHzGG4kSdKiFxEBPB04bNi0hhtJkjTfdouI9a3hdZm5bobLOAT4YWZ+b9iEhhtJ\nkgRA/Pw2ll68YT4WvSkz1/Rdb8RZwIoeo9Zm5mnl8bOAk0dZmeFGkiSNVWYePmh8RCwBngI8ZJTl\neSq4JEla7A4HLs7MkaqVDDeSJGmxeyYjNkmBzVKSJGmRy8znzmR6a24kSVJVDDeSJKkqhhtJklQV\nw40kSaqK4UaSJFXFcCNJkqpiuJEkSVUx3EiSpKoYbiRJUlUMN5IkqSqGG0mSVBXDjSRJqorhRpIk\nVcVwI0mSqmK4kSRJVTHcSJKkqhhuJElSVQw3kiSpKoYbSZJUFcONJEmqiuFGkiRVxXAjSZKqYriR\nJElVMdxIkqSqGG4kSVJVDDeSJKkqhhtJklQVw40kSaqK4UaSJFXFcCNJkqpiuJEkSVUx3EiSpKoY\nbiRJUlUMN5IkqSqGG0mSVBXDjSRJqorhRpIkVcVwI0mSqmK4kSRJVTHcSJKkqhhuJElSVQw3kiSp\nKoYbSZJUFcONJEmqiuFGkiRVZSzhJiLeEBHnR8R5EfG5iNhzHOWQJEmLW0QcFBFfK5lhfUQ8bNg8\n46q5eVtmHpiZBwGnA68dUzkkSdLi9lbg9SUzvLYMDzSWcJOZm1uDOwI5jnJIkqRFL4Gdy+NdgGuG\nzbBkXoszQES8CXg2cAPw2HGVQ5IkLWovAz4bEW+nqZR51LAZInN+Kk0i4ixgRY9RazPztNZ0rwJ2\nyMzX9VnOscCxZfABwAVzXdYK7QZsGnchJoTbajRup9G5rUbjdhrNfpm5fKFWFhGfoXlv5toOwM9b\nw+syc11rvX0zA/A44IuZ+bGIeDpwbGYePmhl8xZuRhURewNnZOYDRph2fWauWYBiTTS30+jcVqNx\nO43ObTUat9No3E4QETcAu2ZmRkQAN2TmzoPmGdfZUvu2Bp8IXDyOckiSpEXvGuAx5fFhwPeGzTCu\nPjdviYj9gF8BVwAvGFM5JEnS4vbHwDsjYglN09axQ6YfT7jJzN+d5azrhk8i3E4z4bYajdtpdG6r\n0bidRjP12ykzvww8ZCbzjL3PjSRJ0lzy9guSJKkqizLcRMSREXFJRFwaEX/VY3xExP8t48+PiIPH\nUc5xG2E7HRoRN5RLVp8XEVN5JeiIOCEifhQRPS8j4P7UGGE7uT8BEbEqIj4fERdFxIUR8Wc9pnGf\nYuRtNfX7VUTsEBHfiIhvle30+h7TuE/NRGYuqj9gO+Ay4N7AUuBbwP27pjkK+DQQwCOAr4+73It0\nOx0KnD7uso77D/hfwMHABX3GT/3+NOJ2cn9qtsMewMHl8XLgux6jtmlbTf1+VfaTncrj7YGvA4/o\nmsZ9agZ/i7Hm5mHApZn5/cy8DfgQcHTXNEcDH8jG14BdI2KPhS7omI2ynQRk5tnATwZM4v7ESNtJ\nQGZem5nnlsc3AhcBe3VN5j7FyNtq6pX95KYyuH356+4Q6z41A4sx3OwFXNUa3sDWH4ZRpqndqNvg\nkaWq89MRccDCFG3iuD+Nzv2pJSL2AR5M80u7zX2qy4BtBe5XRMR2EXEe8CPgzMx0n9oGY7u31ADR\n47nuBDvKNLUbZRucC+ydmTdFxFHAJ4B9t5pL7k+jcX9qiYidgI8BL8stbwYM7lNbGLKt3K+AzPwl\ncFBE7AqcGhEPyMx2/zf3qRlYjDU3G4BVreGVbH0H0FGmqd3QbZCZmztVnZn5KWD7iJiPe4ZMOven\nEbg/3Skitqf5sj4xMz/eYxL3qWLYtnK/2lJmXg98ATiya5T71AwsxnDzTWDfiLhXRCwFngl8smua\nTwLPLr3HH0Fzn4lrF7qgYzZ0O0XEioiI8vhhNO/3jxe8pIuf+9MI3J8aZRu8D7goM/+uz2TuU4y2\nrdyvICJ2LzU2RMRdgcPZ+rZE7lMzsOiapTLz9oh4MfBZmjOCTsjMCyPiBWX8e4BP0fQcvxS4GfjD\ncZV3XEbcTk8FXhgRtwO3AM/MzKmrxoyIk2nOyNgtIjYAr6PpsOf+1DLCdnJ/ajwaOAb4dukjAfBq\nYDW4T3UZZVu5XzVnlf1bRGxHE+5OyczT/d6bPa9QLEmSqrIYm6UkSZJmzXAjSZKqYriRJElVMdxI\nkqSqGG4kSVJVDDeSJKkqhhtpCkTELyPivIi4ICL+o3PBsFks57kR8a7W8Msi4tkDpn9xRHg9DkkL\nynAjTYdbMvOgzHwAzZ2/X7StC4yIJcDzgJMGTHYC8NJtXZckzYThRpo+X6XcTTgi7hMRn4mIcyLi\nSxGxf3n+CRHx9Yj4n4g4KyLu2WM5hwHnlqtl71lqhjp/v4yIvTPzZuDycll9SVoQhhtpipTLuz+O\nO+9Dtg54SWY+BHgF8E/l+S8Dj8jMBwMfAl7ZY3GPBs4ByMxrSs3QQcB7gY9l5hVluvXAIfPwciSp\np0V3bylJ8+Ku5d4++9AEkjMjYifgUcBHyn0LAZaV/yuBD0fEHsBS4Ac9lrkHcFH7iYh4NPBHbBlm\nfgTsPyevQpJGYM2NNB1uKbUqe9OElRfRfP6v79S4lL/fKNP/I/CuzHwg8CfADr2W2X6+BKH3Ac/I\nzJta0+1QppWkBWG4kaZIZt5A08H3FTSB4wcR8TSAaDyoTLoLcHV5/Jw+i7sIuG+Zd3vgFOC4zPxu\n13T3Ay6YsxchSUMYbqQpk5n/A3wLeCbw+8DzI+JbwIXA0WWy42maq74EbOqzqE8D/6s8fhTwUOD1\nrU7Fe5ZxjwbOmvMXIkl9RGaOuwySJlREnAq8MjO/12f8g4G/yMxjFrZkkqaZ4UbSrEXEfsA9M/Ps\nPuOPAL6XmZcvaMEkTTXDjSRJqop9biRJUlUMN5IkqSqGG0mSVBXDjSRJqorhRpIkVeX/A+rNGVGm\n/cggAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "\u003cFigure size 1000x800 with 2 Axes\u003e"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "for degree in [10, 100, 500, 1000]:\n",
        "\n",
        "  Z = jnp.abs(extragradient_residual(100, X + Y * 1j, step, momentum))\n",
        "  Z = Z.at[Z \u003e 1].set(jnp.nan)\n",
        "  plt.figure(figsize=(10, 8))\n",
        "  plt.title('Region of convergence of momentum Extragradient polynomials of degree %s' % degree)\n",
        "  plt.contourf(X, Y, jnp.log(Z))\n",
        "  plt.colorbar()\n",
        "  plt.xlabel('Real(z)')\n",
        "  plt.ylabel('Im(z)')\n",
        "  plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Grsl_zjz7bwl"
      },
      "outputs": [],
      "source": [
        ""
      ]
    }
  ],
  "metadata": {
    "colab": {
      "collapsed_sections": [],
      "last_runtime": {
        "build_target": "//learning/deepmind/public/tools/ml_python:ml_notebook",
        "kind": "private"
      },
      "name": "plot_extragradient.ipynb",
      "provenance": [
        {
          "file_id": "1Nmzj68dD59Oa40QWasWVpUO73eGOOLup",
          "timestamp": 1647352048227
        }
      ]
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}
